Firm Boundaries as Supply Chain Risk Management

Quinta Conferencia de Economistas Costa Rica

José Ignacio González Rojas
j.i.gonzalez-rojas@lse.ac.uk

London School of Economics and Political Science

December 16, 2025

The Question

How Do Firms Set Their Boundaries Under Uninsurable Operational Risk? How Does This Shape Industry Structure?

Post-COVID reality

  • Shocks lasting 1+ month occur every 3.7 years (Lund et al., 2020).
  • 93% of business leaders plan to increase supply chain resilience (Lund et al., 2020).
  • But their strategies seem contradictory from the perspective of firm boundaries:
    • Intel, Samsung, Apple, Ford are specialising ⬆️
    • Hasbro, Nike, Nintendo are fragmenting ⬇️

The puzzle

  • Why do firms facing similar operational risks choose opposite organisational responses?

What’s Been Done ➕ What’s Missing

Theory of the Firm (Antràs, 2003; Bolton & Whinston, 1993; Coase, 1937; S. J. Grossman & Hart, 1986; Hart & Moore, 1990; Kikuchi et al., 2018; Williamson, 1979)

  • Transaction costs ➕ incomplete contracts ➕ ownership rights ➡️ firm boundaries
  • Focus on ex-post adaptation (bargaining, ownership)—what about ex-ante planning under uninsurable risk?

Supply Chain Organisation (Antràs & Chor, 2013; Antràs & de Gortari, 2020; Fally & Hillberry, 2018; Kikuchi et al., 2018)

  • Transaction costs ➕ span-of-control limits ➡️ firms specialise
  • Downstream firms are located in more central locations
  • How do operational risk and production technology alone create boundaries?

Supply Chain Resilience (Castro-Vincenzi, 2024; Elliott et al., 2022; Elliott & Jackson, 2024; G. M. Grossman et al., 2023, 2024; Martinez, 2024)

  • Multisourcing ➕ relationship investment ➕ spatial diversification ➡️ resilience
  • What if risk is uninsurable and firms plan ahead?
  • How do we capture the sequential nature of production and risk?

This Paper

Firm Boundaries Emerge from Technology and Risk

Key Modelling Choices

  1. Sequential production: Stages must complete in order—snakes (Baldwin & Venables, 2013)
  2. Poisson operational failures At rate \(\lambda\) per unit scope, the product is destroyed—uninsurable due to moral hazard ➕ adverse selection
  3. Organisational complexity costs \(c''(\ell) > 0\): Coordination and management costs rise at an increasing rate with scope

Joint Analysis of Firm Boundaries and Industry Structure

  • Firm boundaries: How does operational risk shape optimal vertical scope?
  • Industry structure: How many firms? Where do boundaries fall along the chain?
  • Ex-ante planning perspective: Firms choose boundaries before shocks realise, not adapt after
  • Comparative statics in risk: How do changes in operational risk affect firm boundaries choice and industry structure?

How Risk Shapes Firm Boundaries and Industry Structure

Three mechanisms create finite boundaries

  1. Restart costs: Firms expect to fail \(e^{\lambda \ell}\) times ➡️ must repurchase inputs each time
  2. Organisational constraints: \(c''(\ell) > 0\) ➡️ longer spans harder to manage
  3. Variance benefit ⭐: When firms fail early, they save on costs due to convexity ➡️ encourages longer spans

Non-monotonic response to change in frequency of failures

  • Infrequent: Variance benefit dominates ➡️ risk encourages specialisation
  • Frequent: Restart costs dominate ➡️ risk drives fragmentation
  • Very frequent: Too risky! ➡️ Sequential exit ➡️ upstream firms shut down first

Industry structure reflects risk exposure

  • Endogenous segmentation: Ex-ante identical firms specialise in different production segments
  • Downstream vulnerability: Restart costs scale with input prices \(p(s)\) ➡️ downstream firms more exposed

Intuition: The Pizza Supply Chain 🍕

FIRM 1 Raw Materials FIRM 2 Basic Processing FIRM 3 Assembly & Toppings FIRM 4 Finishing & Delivery Raw Flour Dough ⚠ + Sauce ⚠ + Cheese ⚠ + Toppings ⚠ Bake ⚠ Serve ⚠ 🍕 PIZZA

The Model

The Environment

Sequential stages \(s \in [0,1]\) (Becker & Murphy, 1992; Kikuchi et al., 2018)

  • Cannot produce \(b' > b\) before \(b\)
  • Homogeneous good at each stage

Organisational costs \(c(\ell)\) (Becker & Murphy, 1992; Lucas, 1978)

\[c(0) = 0, \quad c'(0) > 0, \quad c''(\ell) > 0\]

  • Constant returns to scale
  • Decreasing returns to scope (diminishing returns to management)

Operational failures \(U \sim \text{Exp}(\lambda)\) (Kremer, 1993; Sobel, 1992)

  • Complete destruction, no salvage
  • Restart ➡️ buy input from previous firm

Contestable Markets (Baumol, 1982)

  • Technology available to all firms
  • Free entry and exit
  • Zero profits ex ante (entry threat)

Firms Minimise the Number of Production Attempts \(\times\) Expected Cost per Attempt

Bellman equation

\[p(s)=\min_{0 \leq \ell \leq s} \left\{e^{\lambda \ell} \cdot (\tilde{c}(\ell) + p(b))\right\}\]

First-Order Condition

\[\underbrace{p'(b^{*})}_{\text{Marginal profit}} = \underbrace{e^{-\lambda\ell^*}c'(\ell^*)}_{\text{Marginal org cost}} + \underbrace{\lambda[p(b^{*}) + \tilde{c}(\ell^*)]}_{\text{Marginal restart cost}}\]

Comparative Statics

Why Risk Can Encourage Longer Production Runs

Variance benefit is the gap between full cost and average sunk cost

\[VB(\ell) = c(\ell) - \mathbb{E}[c(U)|U<\ell] > 0\]

Expected cost per attempt decomposes into full cost minus variance benefit

\[\begin{align*} \tilde{c}(\ell) &= e^{-\lambda\ell}c(\ell) + (1-e^{-\lambda\ell})\mathbb{E}[c(U)|U<\ell] \\ &= c(\ell) - \underbrace{(1-e^{-\lambda\ell})VB(\ell)}_{\text{Variance benefit reduction}} \end{align*}\]

How does optimal scope \(\ell^{*}\) change with the rate \(\lambda\)?

The effects of more frequent failures is ambiguous
\(\text{sign}\left(\frac{\partial\ell^{*}}{\partial \lambda}\right) = \text{sign}\left(\Psi(\ell^{*}, \lambda)\right)\)

\[\begin{align*} \Psi(\ell, \lambda) &= \frac{\partial \mathbb{P}[\text{success}]}{\partial \lambda}\left(\underbrace{c'(\ell)}_{\substack{\text{direct marginal} \\ \text{cost discount}}}+\underbrace{\lambda VB(\ell)}_{\text{variance benefit}}\right) \\ &+ \underbrace{\lambda\mathbb{P}[\text{failure}]\text{Cov}(U,c(U)|U<\ell)}_{\text{early exit option value}} \\ &- \underbrace{[p(b)+ \tilde{c}(\ell)]}_{\text{total exposure}} \end{align*}\]

Conclusion

Main Contributions

Alternative foundation

  • Technology alone (no contracts)
  • Operational risk + organizational costs

Variance benefit mechanism

  • Counterintuitive: risk can encourage specialisation
  • Depends on cost convexity, hazard rate
  • Three distinct regimes

Position matters

  • Downstream vulnerability emerges naturally
  • Input cost effect drives asymmetry
  • Explains observed restructuring patterns

Industry equilibrium

  • Higher frequency of shocks ➡️ fewer firms
  • Allocative efficient boundaries emerge naturally
  • Firms share risk exposure through prices

Thank you!

References

References

Antràs, P. (2003). Firms, Contracts, and Trade Structure. Quarterly Journal of Economics, 118(4), 1375–1418. https://doi.org/10.1162/003355303322552829
Antràs, P., & Chor, D. (2013). Organizing the Global Value Chain. Econometrica, 81(6), 2127–2204. https://doi.org/10.3982/ECTA10813
Antràs, P., & de Gortari, A. (2020). On the Geography of Global Value Chains. Econometrica, 88(4), 1553–1598. https://doi.org/10.3982/ECTA15362
Baldwin, R., & Venables, A. J. (2013). Spiders and snakes: Offshoring and agglomeration in the global economy. Journal of International Economics, 90(2), 245–254. https://doi.org/10.1016/j.jinteco.2013.02.005
Baumol, W. (1982). Contestable Markets: An Uprising in the Theory of Industry Structure. American Economic Review, 72(1), 1–15. https://doi.org/10.4337/9781035304950
Becker, G. S., & Murphy, K. M. (1992). The Division of Labor, Coordination Costs, and Knowledge. Quarterly Journal of Economics, 107(4), 1137–1160. https://doi.org/10.2307/2118383
Bolton, P., & Whinston, M. D. (1993). Incomplete Contracts, Vertical Integration, and Supply Assurance. Review of Economic Studies, 60(1), 121. https://doi.org/10.2307/2297815
Castro-Vincenzi, J. (2024). Climate Hazards and Resilience in the Global Car Industry [Working Paper].
Coase, R. H. (1937). The Nature of the Firm. Economica, 4(16), 386–405. https://doi.org/10.1111/j.1468-0335.1937.tb00002.x
Elliott, M., Golub, B., & Leduc, M. V. (2022). Supply Network Formation and Fragility. American Economic Review, 112(8), 2701–2747. https://doi.org/10.1257/aer.20210220
Elliott, M., & Jackson, M. O. (2024). Supply Chain Disruptions, the Structure of Production Networks, and the Impact of Globalization [Working Paper].
Fally, T., & Hillberry, R. (2018). A Coasian model of international production chains. Journal of International Economics, 114, 299–315. https://doi.org/10.1016/j.jinteco.2018.07.001
Grossman, G. M., Helpman, E., & Lhuillier, H. (2023). Supply Chain Resilience: Should Policy Promote International Diversification or Reshoring? Journal of Political Economy, 131(12), 3462–3496. https://doi.org/10.1086/725173
Grossman, G. M., Helpman, E., & Sabal, A. (2024). Optimal Resilience in Multitier Supply Chains. Quarterly Journal of Economics, 139(4), 1–49. https://doi.org/10.1093/qje/qjae024
Grossman, S. J., & Hart, O. D. (1986). The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration. Journal of Political Economy, 94(4), 691–719. https://doi.org/10.1086/261404
Hart, O., & Moore, J. (1990). Property Rights and the Nature of the Firm. Journal of Political Economy, 98(6), 11191158.
Kikuchi, T., Nishimura, K., & Stachurski, J. (2018). Span of control, transaction costs, and the structure of production chains. Theoretical Economics, 13(2), 729–760. https://doi.org/10.3982/TE2376
Kremer, M. (1993). The O-Ring Theory of Economic Development. Quarterly Journal of Economics, 108(3), 551–575. https://doi.org/10.2307/2118400
Lucas, R. E. (1978). On the Size Distribution of Business Firms. Bell Journal of Economics, 9(2), 508–523. https://doi.org/10.2307/3003596
Lund, S., Maryika, J., Woetzel, J., Barriball, E., Krishnan, M., Alicke, K., Birshan, M., George, K., Smit, S., Swan, D., & Hutzler, K. (2020). Risk, resilience, and rebalancing in global value chains [Report]. McKinsey Global Institute. https://www.mckinsey.com/capabilities/operations/our-insights/risk-resilience-and-rebalancing-in-global-value-chains
Martinez, A. (2024). Trade Relationships During and After a Crisis: Evidence from Road Disruptions in Colombian Flower Exports [Working Paper].
Sobel, J. (1992). How to Count to One Thousand. The Economic Journal, 102(410), 1. https://doi.org/10.2307/2234847
Williamson, O. E. (1979). Transaction-Cost Economics: The Governance of Contractual Relations. Journal of Law and Economics, 22(2), 233–261. https://doi.org/10.1086/466942